Lab #1:measuring g
Time an object under free fall  gravitational acceleration g
If object falls starting from rest:

v(t )  gt
1 2 x(t )  gt
2

 Plotting velocity (y axis) vs. time (x axis) should have a slope of g
Fill out pre-lab sheet available at http://physics.msstate.edu/labs

Vectors – geometric objects that are independent of any coordinate system  3
ˆ
ˆ
A   Ai ei  Ai ei

ˆ ˆ ei  e j  ij

i 1

Einstein summation convention

Scalar (or dot) product of 2 vectors

 
A B 

AB

i 1..3

i

i

!!! Scalar quantity - invariant under the rotation of coordinate system !!!

Cross (or vector) product of 2 vectors

  

C  A  B  C  AB sin n

Angle b/w A and B

 
 
A  B  B  A

Defining the direction of the normal vector in cross product

Chapter 21
Electric charge and electric field

Electricity and Magnetism, Some History: 1
• Many applications
– Macroscopic and microscopic
• Chinese
– Documents suggest that magnetism was observed as early as 2000 BC
• Greeks
– Electrical and magnetic phenomena as early as 700
BC
– Experiments with amber and magnetite
• 1600: - William Gilbert showed electrification effects were not confined to just amber
– the electrification effects were a general phenomena

Electricity and Magnetism, Some History: 2
• 1785
– Charles Coulomb confirmed inverse square law form for electric forces
• 1819
– Hans Oersted found a compass needle deflected when near a wire carrying an electric current
• 1831
– Michael Faraday and Joseph Henry showed that when a wire is moved near a magnet, an electric current is produced in the wire

Electricity and Magnetism, Some History: 3

• 1873
– James Clerk Maxwell used observations and other experimental facts as a basis for formulating the laws of electromagnetism • Unified electricity and magnetism
• 1888
– Heinrich Hertz verified Maxwell’s predictions
– He produced electromagnetic waves

Electric Charges: basic properties
 There are two kinds of electric charges: positive – protons, negative - electrons
Particle

Symbol Charge

Mass

Electron

-1

1

Proton

p

+1

1836.15

Neutron



en

0

1838.68

The electric charge, q, is quantized
– q is the standard